The US Park Police can and do enforce basic traffic regulations in national parks - which includes some roads, like the Blue Ridge Parkway, that are “linear parks”. In respect of the fact that these roads are often used by local traffic, they will generally permit things that would be legal under the law of the state you are in (e.g., concealed firearm carry, so long as it’s in the car and not brought into a ranger station or other building on the federal property).